research-article

Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams

Author:

C. KrattenthalerAuthors Info & Claims

Journal of Combinatorial Theory Series A, Volume 144, Issue C

Pages 277 - 291

https://doi.org/10.1016/j.jcta.2016.06.015

Published: 01 November 2016 Publication History

Abstract

We prove that the number of oscillating tableaux of length n with at most k columns, starting at ź and ending at the one-column shape ( 1 m ), is equal to the number of standard Young tableaux of size n with m columns of odd length, all columns of length at most 2k. This refines a conjecture of Burrill, which it thereby establishes. We prove as well a "Knuth-type" extension stating a similar equi-enumeration result between generalised oscillating tableaux and semistandard tableaux.

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Cited By

Courtiel JFusy ELepoutre MMishna M(2018)Bijections for Weyl Chamber walks ending on an axis, using arc diagrams and Schnyder woodsEuropean Journal of Combinatorics10.1016/j.ejc.2017.10.00369:C(126-142)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1016/j.ejc.2017.10.003

Index Terms

Bijections between oscillating tableaux and (semi)standard tableaux via growth diagrams
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
      1. Permutations and combinations
2. Theory of computation
  1. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

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cover image Journal of Combinatorial Theory Series A

Journal of Combinatorial Theory Series A Volume 144, Issue C

November 2016

512 pages

ISSN:0097-3165

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Copyright © Elsevier Inc.

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Academic Press, Inc.

United States

Publication History

Published: 01 November 2016

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Cited By

Courtiel JFusy ELepoutre MMishna M(2018)Bijections for Weyl Chamber walks ending on an axis, using arc diagrams and Schnyder woodsEuropean Journal of Combinatorics10.1016/j.ejc.2017.10.00369:C(126-142)Online publication date: 1-Mar-2018
https://dl.acm.org/doi/10.1016/j.ejc.2017.10.003

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